F = ma

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In Free-fall
Fg
Fg
Fg
F ma a F/m
Fg
Fg
so acceleration must be constant
Fg
Fg
2
Free-fall
An object in free-fall is only subject to the
force of gravity (weight)
Fnet Fg
(Neglect Air Resistance)
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Galileo
Galileo dropped two cannon balls of different
weights from the top of Leaning Tower of Piza.
The two cannon balls reached the ground at the
same time. He proved that when objects of
different weights are dropped at the same height
and time, they take the same amount of time to
fall to the ground (ignoring air resistance).
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Using Newtons second law, we can conclude that
the force of gravity on an object is proportional
to the mass of the object.
Yes, They Rounded!
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Important!
Since the acceleration of gravity is down, when
in free-fall, ignoring air resistance g a
- 9.8 m/s2
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What observations can you make about the picture?
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?y ½at2
?v a?t If vi and ti are equal to Zero vf at
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Free-Fall Motion
A 1-kg rock is thrown into the air at 10 m/s
upward. Neglecting air resistance, what is the
net force acting on the rock?
Answer In the absence of air resistance, the
only force exerted on the 1 kg rock is simply the
force due to gravity, mg, at any speed along its
trajectory! Net Force mg (9.8m/s2)(1kg)
9.8N
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Remember g -10 m/s2
0 m/s
10 m/s
- 10 m/s
20 m/s
- 20 m/s
30 m/s
- 30 m/s
Ignoring Air Resistance
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Sign Conventions for Free-Fall
A B C D
-

0
0
Dy v a
-
-

0
Up Down -
-9.8
-9.8
-9.8
-9.8

• At point A the change in y is 0, the velocity is
  positive.
• At point B the change in y is positive, the
  velocity is zero.
• At point C the change in y is 0, the velocity is
  negative.
• At point D, the change in y is negative, the
  velocity is negative.
• The acceleration for all the points is -9.8 m/s2

Zero Reference Point
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Remember Motion Graphs?
Object is slowing down - acceleration velocity
x
v
t
Object is speeding up - acceleration - velocity
t
a
t
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• Which object hits the ground first? (ignore air
  friction)
• Which object hits the ground first when we
  include air friction?

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With Air Resistance
No Air Resistance
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Why did air resistance slow down the feather so
much and not the elephant?
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So what is
Terminal Velocity?
Well, eventually, the force of air resistance
becomes large enough to balance the force of
gravity. At this instant in time, the net force
is 0 Newtons the object stops accelerating. The
object is said to have "reached a terminal
velocity."
Fg FR a 0 m/s2
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Skydiving Observe the motion of the skydiver
below. As the skydiver falls, he encounters the
force of air resistance. The amount of air
resistance is dependent upon two
variables the speed of the skydiver, and
the cross-sectional area of the skydiver.

• Draw FBDs at the following points. Describe the
  direction of the net force, acceleration, and
  velocity.
• Just released from the helicopter.
• Falling for a few seconds.
• Falling for a few seconds more to a point where
  the air resistance force equals the gravitational
  force.
• Deployment of a parachute.
• Repeat of (3) for the parachute.
• Now draw velocity and acceleration motion map
  showing the motion.

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Parachutes
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• Find the acceleration for A, B, C, and D.
• a (Fnet / m) (1000 N) / (100 kg) 10 m/s/s
• a (Fnet / m) (600 N) / (100 kg) 6 m/s/s
• a (Fnet / m) (200 N) / (100 kg) 2 m/s/s
• a (Fnet/m) (0 N) / (100 kg) 0 m/s/s.

Which diagram represents terminal velocity?
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Air Resistance

• A sky diver in the spread-eagle position opens
  the parachute. (She has reached terminal velocity
  before she opens the parachute)
• Is the diver accelerated?
• Which direction? Explain your answer.

Yes, she is accelerated in the upward direction.
She is slowing down, yet still falling.

• As an object falls through air, it usually
  encounters some degree of air resistance.
• The actual amount of air resistance encountered
  by an object depends upon a variety of factors.
• The two most common factors which have a direct
  effect upon the amount of air resistance present
  are the speed of the object and the
  cross-sectional area of the object. Increased
  speeds result in an increased amount of air
  resistance. Increased cross-sectional areas
  result in an increased amount of air resistance.

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Watch This!
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In situations in which there is air resistance,
massive objects fall faster than less massive
objects. Why?
Massive objects fall faster than less massive
objects because they are acted upon by a larger
force of gravity for this reason, they
accelerate to higher speeds until the air
resistance force equals their gravity force.
Basically the more massive object accelerates
longer before reaching terminal velocity.
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Free-Fall Practice

1. Draw Picture
2. List Givens
3. Write Equations
4. Solve For Unknowns

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Fun Problems!!!!

• 1) A penny is dropped from the top of a
  rollercoaster. The height of the ride is 110m.
  (neglect air resistance)
• Find the speed of the penny when it hits the
  ground.
• Find the time it takes for the penny to fall to
  the ground.
• Would it be different for a quarter?
• (how about with air resistance?)

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• 2) A stone is thrown straight upward with a speed
  of 20 m/s.
• a) How high does it go?
• b) How long does it take to rise to its
  maximum
• height?

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• 3) An object is thrown straight upward and falls
  back to the thrower after a round trip time of
  0.80 s.
• How fast was the object thrown?

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• 4)A cell phone is thrown upward from the edge of
  a building with a velocity of 20 m/s.
• Where will the object be at 3s after it is
  thrown?
• After 5s.?

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• 5) George throws an apple vertically upward from
  a height of 1.3 m with an initial velocity of 24
  m/s.
• Will the apple reach a friend in a tree
  5.3 m above the ground?
• If the apple is not caught, how long
  will the apple be in the air before it
  hits the ground?